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EXAMPLE 1

( x , y ) (2 x , 2 y ). A (2, 1) L (4, 2). B (4, 1) M (8, 2). C (4, –1) N (8, –2). D (1, –1) P (2, –2). EXAMPLE 1. Draw a dilation with a scale factor greater than 1.

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EXAMPLE 1

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  1. (x, y) (2x, 2y) A(2, 1) L(4, 2) B(4, 1) M(8, 2) C(4, –1) N(8, –2) D(1, –1) P(2, –2) EXAMPLE 1 Draw a dilation with a scale factor greater than 1 Draw a dilation of quadrilateralABCDwith verticesA(2, 1), B(4, 1), C(4, – 1), andD(1, – 1). Use a scale factor of2. SOLUTION First draw ABCD. Find the dilation of each vertex by multiplying its coordinates by 2. Then draw the dilation.

  2. A triangle has the vertices A(4,– 4),B(8, 2), and C(8,– 4). The image of ABCafter a dilation with a scale factor of is DEF. SketchABCandDEF. Verify that ABCand DEFare similar. 1 a. 2 b. EXAMPLE 2 Verify that a figure is similar to its dilation

  3. a. The scale factor is less than one, so the dilation is a reduction. 1 1 2 2 A(4, – 4) D(2, – 2) y x, (x, y) C(8, – 4) F(4, – 2) B(8, 2) E(4, 1) EXAMPLE 2 Verify that a figure is similar to its dilation SOLUTION

  4. b. Because Cand Fare both right angles, C F. Show that the lengths of the sides that include Cand Fare proportional. Find the horizontal and vertical lengths from the coordinate plane. ? = AC BC = 4 6 EF DF So, the lengths of the sides that include Cand Fare proportional. 2 3 ANSWER Therefore, ABCDEFby the SAS Similarity Theorem. ~ EXAMPLE 2 Verify that a figure is similar to its dilation

  5. Find the coordinates of L, M, and N so that LMN is a dilation of PQR with a scale factor of k. Sketch PQR and LMN. x, y = 4x , 4y P (–2, –1) = L (–8, –4) M (– 4, 0) Q (–1, 0) = R (0, –1) = N (0, –4) for Examples 1 and 2 GUIDED PRACTICE 1. P(–2, 21), Q(–1, 0), R(0, –1); k = 4 SOLUTION Find the dilation of each vertex by multiplying its coordinates by 4. ANSWER

  6. 2 2 5 5 x, y x , y P(5, –5) L (2, –2) Q(10,–2) M (4, –2) R (10, 5) N (4, 2) for Examples 1 and 2 GUIDED PRACTICE 2. P(5, –5), Q(10, –5), R(10, 5); k = 0.4 SOLUTION Find the dilation of each vertex by multiplying its coordinates by 0.4. The scale is less than one, so the dilation is a reduction. ANSWER

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